Webentire cake by choosing to cut pieces [0; ];[ ;1]. In this paper we consider the design of truthful and fair cake cutting algorithms. To the best of our knowledge we are the first to do so.3 However, there is a major obstacle that must be circumvented: regardless of … Fair cake-cutting is a kind of fair division problem. The problem involves a heterogeneous resource, such as a cake with different toppings, that is assumed to be divisible – it is possible to cut arbitrarily small pieces of it without destroying their value. The resource has to be divided among several partners who … See more There is a cake C, which is usually assumed to be either a finite 1-dimensional segment, a 2-dimensional polygon or a finite subset of the multidimensional Euclidean plane R . There are n people … See more Proportionality The original and most common criterion for justice is proportionality (PR). In a proportional cake-cutting, each person receives a piece that he values as at least 1/n of the value of the entire cake. In the example cake, a … See more In addition to the desired properties of the final partitions, there are also desired properties of the division process. One of these properties is … See more Reasoning about the run-time complexity of algorithms requires a model of computation. Several such models are common in the … See more In some cases, the pieces allocated to the partners must satisfy some geometric constraints, in addition to being fair. • The most common constraint is connectivity. In case the "cake" is a 1-dimensional interval, this translates to the requirement that … See more In addition to justice, it is also common to consider the economic efficiency of the division; see efficient cake-cutting. There are several levels of efficiency: • The weaker notion is Pareto efficiency. It can be easily satisfied by just giving the entire cake to a … See more There is a generalization of the cake-cutting problem in which there are several cakes, and each agent needs to get a piece in each cake. See more

[1810.08243] Fair Cake-Cutting in Practice - arXiv.org

WebCutting a cake, dividing up the property in an estate, determining the borders in an international dispute - such problems of fair division are ubiquitous. Fair Division treats all these problems and many more through a rigorous analysis of a variety of procedures for allocating goods (or 'bads' like chores), or deciding who wins on what issues ... WebIn the mathematics of social science, and especially game theory, a moving-knife procedure is a type of solution to the fair division problem. The canonical example is the division of a cake using a knife.. The simplest example is a moving-knife equivalent of the I cut, you choose scheme, first described by A.K.Austin as a prelude to his own procedure:. One … heriot canvas

Fair pie-cutting - Wikipedia

WebApr 22, 2024 · Fair cake-cutting is a kind of fair division problem. The problem involves a heterogeneous resource, such as a cake with different toppings, that is assumed to be divisible – it is possible to cut arbitrarily small pieces of it without destroying their value. WebApr 13, 2024 · This page explores the mathematical results on fair division since the 1940s, when Hugo Steinhaus began the mathematically rigorous study of this problem. ... As we have shown, the cake cutting problem … WebOnline arrival of people The party cake-cutting problem. Walsh studies an online variant of fair cake-cutting, in which agents arrive and depart during the division process, like in a party.Well-known fair division procedures like divide and choose and the Dubins-Spanier moving-knife procedure can be adapted to this setting. They guarantee online variants of … mattress firm englewood co